{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lecture 24 - Sequential Monte Carlo in `PyMC3`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "import theano as T\n",
    "from theano import shared, function, tensor as tt\n",
    "from sample_smc import sample_smc \n",
    "\n",
    "try:\n",
    "    import sympy\n",
    "except:\n",
    "    _=!pip install sympy\n",
    "    import sympy\n",
    "\n",
    "import matplotlib.pyplot as plt \n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "\n",
    "import logging\n",
    "\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Objectives\n",
    "\n",
    "+ Compute the model evidence using `PyMC3`.\n",
    "+ Do model selection with `PyMC3`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sanity check - Does the calculation of the evidence with PySMC work?\n",
    "\n",
    "Let\n",
    "$$\n",
    "p(\\theta) = \\mathcal{N}(\\theta|0, 1),\n",
    "$$\n",
    "and\n",
    "$$\n",
    "p(y|\\theta) = \\mathcal{N}(y|\\theta,0).\n",
    "$$\n",
    "The posterior of $\\theta$ given $y$ is:\n",
    "$$\n",
    "p(\\theta|y) = \\frac{p(y|\\theta)p(\\theta)}{Z},\n",
    "$$\n",
    "where\n",
    "$$\n",
    "Z = \\int_{-\\infty}^{\\infty} p(y|\\theta)p(\\theta)d\\theta.\n",
    "$$\n",
    "Let's first calculate $Z$ analytically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{0.5 e^{- 0.25 y^{2}}}{\\sqrt{\\pi}}$"
      ],
      "text/plain": [
       "            2\n",
       "     -0.25⋅y \n",
       "0.5⋅ℯ        \n",
       "─────────────\n",
       "      √π     "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy.stats\n",
    "sympy.init_printing()\n",
    "y, t = sympy.symbols('y \\\\theta')\n",
    "q = 1. / sympy.sqrt(2. * sympy.pi) * sympy.exp(-0.5 * (y - t) ** 2) * \\\n",
    "    1. / sympy.sqrt(2. * sympy.pi) * sympy.exp(-0.5 * t ** 2)\n",
    "sympy.simplify(sympy.integrate(q, (t, -sympy.oo, sympy.oo)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, if the observed $y$ was zero, then the Z should be:\n",
    "$$\n",
    "Z = \\frac{1}{2\\sqrt{\\pi}}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "log Z = -1.266\n"
     ]
    }
   ],
   "source": [
    "Z = 1 /  2. / np.sqrt(np.pi)\n",
    "print('log Z = {0:.3f}'.format(np.log(Z)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All, right. Now, let's program this thing in pysmc and compare the results.\n",
    "\n",
    "We start with the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sample initial stage: ...\n",
      "Stage:   0 Beta: 1.000 Steps:  25 Acce: 1.000\n"
     ]
    }
   ],
   "source": [
    "model = pm.Model()\n",
    "yobs = 0.\n",
    "with model:\n",
    "    # prior over theta \n",
    "    theta = pm.Normal('theta', mu=0., sigma=1.,testval=0.)\n",
    "    \n",
    "    # log likelihood \n",
    "    llk = pm.Potential('llk', pm.Normal.dist(theta, 1.).logp(yobs))\n",
    "    \n",
    "    trace, smcres = sample_smc(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True log evidence: -1.2655 \n",
      "SMC log evidence: -1.2880\n"
     ]
    }
   ],
   "source": [
    "# get the model evidence \n",
    "log_evidence_smc = np.log(smcres.model.marginal_likelihood)\n",
    "print('True log evidence: %.4f \\nSMC log evidence: %.4f'%(np.log(Z), log_evidence_smc))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which is close to the truth."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Questions\n",
    "\n",
    "+ Repeat the calculations above for a varying number of SMC particles. Start from 10 and go up to 10,000."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polynomial Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_design_matrix(X, phi):\n",
    "    \"\"\"\n",
    "    Arguments:\n",
    "    \n",
    "    X   -  The observed inputs (1D array)\n",
    "    phi -  The basis functions.\n",
    "    \"\"\"\n",
    "    num_observations = X.shape[0]\n",
    "    num_basis = phi.num_basis\n",
    "    Phi = np.ndarray((num_observations, num_basis))\n",
    "    for i in range(num_observations):\n",
    "        Phi[i, :] = phi(X[i, :])\n",
    "    return Phi\n",
    "\n",
    "class PolynomialBasis(object):\n",
    "    \"\"\"\n",
    "    A set of linear basis functions.\n",
    "    \n",
    "    Arguments:\n",
    "    degree  -  The degree of the polynomial.\n",
    "    \"\"\"\n",
    "    def __init__(self, degree):\n",
    "        self.degree = degree\n",
    "        self.num_basis = degree + 1\n",
    "    def __call__(self, x):\n",
    "        return np.array([x[0] ** i for i in range(self.degree + 1)])\n",
    "    \n",
    "\n",
    "class FourierBasis(object):\n",
    "    \"\"\"\n",
    "    A set of linear basis functions.\n",
    "    \n",
    "    Arguments:\n",
    "    num_terms  -  The number of Fourier terms.\n",
    "    L          -  The period of the function.\n",
    "    \"\"\"\n",
    "    def __init__(self, num_terms, L):\n",
    "        self.num_terms = num_terms\n",
    "        self.L = L\n",
    "        self.num_basis = 2 * num_terms\n",
    "    def __call__(self, x):\n",
    "        res = np.ndarray((self.num_basis,))\n",
    "        for i in range(num_terms):\n",
    "            res[2 * i] = np.cos(2 * i * np.pi / self.L * x[0])\n",
    "            res[2 * i + 1] = np.sin(2 * (i+1) * np.pi / self.L * x[0])\n",
    "        return res\n",
    "    \n",
    "\n",
    "class RadialBasisFunctions(object):\n",
    "    \"\"\"\n",
    "    A set of linear basis functions.\n",
    "    \n",
    "    Arguments:\n",
    "    X   -  The centers of the radial basis functions.\n",
    "    ell -  The assumed lengthscale.\n",
    "    \"\"\"\n",
    "    def __init__(self, X, ell):\n",
    "        self.X = X\n",
    "        self.ell = ell\n",
    "        self.num_basis = X.shape[0]\n",
    "    def __call__(self, x):\n",
    "        return np.exp(-.5 * (x - self.X) ** 2 / self.ell ** 2).flatten()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's generate some fake data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(12345)\n",
    "def getdata(N, sigma2):\n",
    "    X = 2 * np.random.rand(N) - 1.\n",
    "    y = 0.5 * X  ** 3 - 0.3 * X ** 2 + np.sqrt(sigma2) * np.random.rand(N)\n",
    "    return X, y\n",
    "\n",
    "num_samples = 50\n",
    "sigma2 = 1e-3\n",
    "X, y = getdata(num_samples, sigma2)\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(X, y, 'o', markeredgewidth=2, label='Data')\n",
    "plt.xlabel('$x$', fontsize=20)\n",
    "plt.ylabel('$y$', fontsize=20)\n",
    "plt.legend(loc='best', fontsize=20)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are going to implement a standard Bayesian linear regression and train it with `PyMC3`.\n",
    "We will compute the evidence in order to select the best class of basis functions.\n",
    "The model is as follows:\n",
    "\n",
    "The output $y$ conditioned on the input $x$, the weights of the basis functions $w$ and\n",
    "the noise variance $\\sigma^2$ has likelihood:\n",
    "$$\n",
    "p(y|x,w,\\sigma, \\mathcal{M}) = \\mathcal{N}(y|w^T\\phi_{\\mathcal{M}}(x), \\sigma^2),\n",
    "$$\n",
    "where $\\phi_{\\mathcal{M},1}(\\cdot), \\dots, \\phi_{\\mathcal{M},m_{\\mathcal{M}}}(\\cdot)$ are the\n",
    "$m_{\\mathcal{M}}$ basis functions of the model $\\mathcal{M}$.\n",
    "We put a normal prior on the weights:\n",
    "$$\n",
    "p(w|\\alpha) = \\mathcal{N}(w|0, \\alpha I_{m_{\\mathcal{M}}}),\n",
    "$$\n",
    "and an inverse Gamma prior for $\\sigma$ and $\\alpha$:\n",
    "$$\n",
    "p(\\sigma^2) = \\mathrm{IG}(\\sigma^2|1, 1),\n",
    "$$\n",
    "and\n",
    "$$\n",
    "p(\\alpha) = \\mathrm{IG}(\\alpha|1,1).\n",
    "$$\n",
    "\n",
    "Assume that the data we have observed are:\n",
    "$$\n",
    "x_{1:n} = \\{x_1,\\dots,x_n\\},\\;\\mathrm{and}\\;y_{1:n} = \\{y_1,\\dots,y_n\\}.\n",
    "$$\n",
    "Consider the design matrix $\\Phi_{\\mathcal{M}}\\in\\mathbb{R}^{n\\times m}$:\n",
    "$$\n",
    "\\Phi_{\\mathcal{M},ij} = \\phi_{\\mathcal{M},j}(x_i).\n",
    "$$\n",
    "The likelihood of the data is:\n",
    "$$\n",
    "p(y_{1:n} | x_{1:n}, w, \\sigma, \\mathcal{M}) = \\mathcal{N}(y_{1:n}|\\Phi_{\\mathcal{M}}w, \\sigma^2I_n).\n",
    "$$\n",
    "Let's turn this into `PyMC3` code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_model(Phi, y):\n",
    "    \"\"\"\n",
    "    INPUTS:\n",
    "        Phi -> Design matrix.\n",
    "        y   -> Target vector. \n",
    "        \n",
    "    RETURNS:\n",
    "        model -> `pymc3.model` context.\n",
    "    \"\"\"\n",
    "    num_data, num_features = Phi.shape\n",
    "    \n",
    "    # define the model \n",
    "    with pm.Model() as model:\n",
    "        # prior on the weights \n",
    "        alpha = pm.InverseGamma('alpha', alpha=1., beta=1.)\n",
    "        w = pm.Normal('w', mu=0., tau=alpha, shape=num_features)\n",
    "        \n",
    "        # prior on the likelihood noise variance \n",
    "        sigma2 = pm.InverseGamma('sigma2', alpha=5., beta=0.1)\n",
    "        \n",
    "        # the data likelihood mean \n",
    "        ymean = pm.Deterministic('ymean', tt.dot(Phi, w))\n",
    "        \n",
    "        # likelihood \n",
    "        y = pm.Normal('y', ymean, sigma2, shape=num_data, observed=y)\n",
    "        #llk = pm.Potential('llk', pm.Normal.dist(ymean, tt.sqrt(sigma2)).logp_sum(y))\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's create a function that trains the model using pysmc for a polynomial basis with a given order."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sample initial stage: ...\n",
      "Stage:   0 Beta: 0.000 Steps:  25 Acce: 1.000\n",
      "\n",
      "  0%|          | 0/100 [00:00<?, ?it/s]\u001b[A\n",
      "100%|██████████| 100/100 [00:00<00:00, 933.04it/s][A\n",
      "Stage:   1 Beta: 0.000 Steps:  25 Acce: 0.155\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1061.16it/s]\n",
      "Stage:   2 Beta: 0.000 Steps:  25 Acce: 0.159\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1048.84it/s]\n",
      "Stage:   3 Beta: 0.000 Steps:  25 Acce: 0.197\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1242.81it/s]\n",
      "Stage:   4 Beta: 0.001 Steps:  21 Acce: 0.257\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1725.92it/s]\n",
      "Stage:   5 Beta: 0.001 Steps:  15 Acce: 0.289\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1986.61it/s]\n",
      "Stage:   6 Beta: 0.002 Steps:  13 Acce: 0.276\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1770.82it/s]\n",
      "Stage:   7 Beta: 0.004 Steps:  14 Acce: 0.211\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1358.40it/s]\n",
      "Stage:   8 Beta: 0.006 Steps:  19 Acce: 0.228\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1510.53it/s]\n",
      "Stage:   9 Beta: 0.011 Steps:  17 Acce: 0.246\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1636.34it/s]\n",
      "Stage:  10 Beta: 0.017 Steps:  16 Acce: 0.196\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1238.94it/s]\n",
      "Stage:  11 Beta: 0.025 Steps:  21 Acce: 0.250\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1612.00it/s]\n",
      "Stage:  12 Beta: 0.035 Steps:  16 Acce: 0.244\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1618.49it/s]\n",
      "Stage:  13 Beta: 0.050 Steps:  16 Acce: 0.196\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1229.92it/s]\n",
      "Stage:  14 Beta: 0.068 Steps:  21 Acce: 0.285\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1966.60it/s]\n",
      "Stage:  15 Beta: 0.090 Steps:  13 Acce: 0.313\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 2164.50it/s]\n",
      "Stage:  16 Beta: 0.116 Steps:  12 Acce: 0.338\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 2285.18it/s]\n",
      "Stage:  17 Beta: 0.151 Steps:  11 Acce: 0.289\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1935.20it/s]\n",
      "Stage:  18 Beta: 0.192 Steps:  13 Acce: 0.278\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1840.10it/s]\n",
      "Stage:  19 Beta: 0.240 Steps:  14 Acce: 0.272\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1826.72it/s]\n",
      "Stage:  20 Beta: 0.298 Steps:  14 Acce: 0.264\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1681.72it/s]\n",
      "Stage:  21 Beta: 0.378 Steps:  15 Acce: 0.276\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1877.26it/s]\n",
      "Stage:  22 Beta: 0.479 Steps:  14 Acce: 0.289\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1988.47it/s]\n",
      "Stage:  23 Beta: 0.610 Steps:  13 Acce: 0.272\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1843.80it/s]\n",
      "Stage:  24 Beta: 0.816 Steps:  14 Acce: 0.252\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1749.14it/s]\n",
      "Stage:  25 Beta: 1.000 Steps:  15 Acce: 0.261\n",
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 1668.52it/s]\n"
     ]
    }
   ],
   "source": [
    "def fit_poly(phi, X, y, num_particles=100):\n",
    "    \"\"\"\n",
    "    \n",
    "    RETURNS:\n",
    "        1. An instance of pymc3.Model for the SMC model.\n",
    "        2. The SMC trace.\n",
    "        3. An instance of pymc3.smc.SMC containing sampling information.\n",
    "    \"\"\"\n",
    "    Phi = compute_design_matrix(X[:, None], phi)\n",
    "    smcmodel = make_model(Phi, y)\n",
    "    trace, res = sample_smc(draws=num_particles, \n",
    "                         model=smcmodel, \n",
    "                         progressbar=True, \n",
    "                         threshold=0.8)\n",
    "    return smcmodel, trace, res\n",
    "\n",
    "phi = PolynomialBasis(3)\n",
    "model, trace, res = fit_poly(phi, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Postprocessing \n",
    "\n",
    "Once you have the `trace` object for the SMC simulation you can apply all the standard postprocessing tools from `PyMC3` as usual. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the posterior distribution over the weights precision and the the likelihood noise, $\\alpha$ and $\\sigma^2$ respectively:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 993.6x331.2 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_=pm.plot_posterior(trace, var_names=['alpha', 'sigma2'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the posterior predictive mean of the output $y$, i.e., $\\mathbb{E}[y|x, w, \\sigma]$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "100%|██████████| 100/100 [00:00<00:00, 3874.47it/s]\n"
     ]
    }
   ],
   "source": [
    "ppsamples = pm.sample_posterior_predictive(model=model, \n",
    "                               trace=trace, var_names=['ymean'])['ymean']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = np.argsort(X)\n",
    "plt.figure(figsize=(10, 8))\n",
    "plt.plot(X[idx], ppsamples.mean(0)[idx], linewidth=2.5, label='Posterior Predictive Mean' )\n",
    "plt.plot(X, y, 'x', markeredgewidth=2.5, markersize=10, label='Observed data')\n",
    "\n",
    "plt.legend(loc='best', fontsize=20)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SMC does a particle approximation of the posterior distribution. The particles themselves can be obtained from the `trace` object and the particle weights can be obtained from the  `res` object. \n",
    "\n",
    "Recall that the approximate posterior distribution is of the form $p(\\theta|\\mathcal{D}) = \\sum_{j=1}^{N} w_j \\delta(\\theta - \\theta_j)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "particles_w = trace.w\n",
    "particles_alpha = trace.alpha\n",
    "particle_weights = res.weights   # <- these are the ws from the above equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model comparison"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since SMC can approximate the model evidence it provides a principled way of comparing models. Let's compare 5 different polynomial regression models where we change the degree of the polynomial from 1 to 5. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sample initial stage: ...\n",
      "Stage:   0 Beta: 0.000 Steps:  25 Acce: 1.000\n",
      "\n",
      "  0%|          | 0/500 [00:00<?, ?it/s]\u001b[A\n",
      " 21%|██▏       | 107/500 [00:00<00:00, 1069.53it/s]\u001b[A\n",
      " 43%|████▎     | 214/500 [00:00<00:00, 1067.47it/s]\u001b[A\n",
      " 64%|██████▍   | 319/500 [00:00<00:00, 1061.39it/s]\u001b[A\n",
      "100%|██████████| 500/500 [00:00<00:00, 1060.87it/s]\u001b[A\n",
      "Stage:   1 Beta: 0.000 Steps:  25 Acce: 0.288\n",
      "\n",
      "  0%|          | 0/500 [00:00<?, ?it/s]\u001b[A\n",
      " 41%|████      | 203/500 [00:00<00:00, 2027.15it/s]\u001b[A\n",
      "100%|██████████| 500/500 [00:00<00:00, 2003.37it/s]\u001b[A\n",
      "Stage:   2 Beta: 0.000 Steps:  13 Acce: 0.259\n",
      "\n",
      "  0%|          | 0/500 [00:00<?, ?it/s]\u001b[A\n",
      " 36%|███▌      | 180/500 [00:00<00:00, 1799.16it/s]\u001b[A\n",
      "100%|██████████| 500/500 [00:00<00:00, 1763.08it/s]\u001b[A\n",
      "Stage:   3 Beta: 0.000 Steps:  15 Acce: 0.271\n",
      "\n",
      "  0%|          | 0/500 [00:00<?, ?it/s]\u001b[A\n",
      " 37%|███▋      | 187/500 [00:00<00:00, 1869.01it/s]\u001b[A\n",
      "100%|██████████| 500/500 [00:00<00:00, 1860.91it/s]\u001b[A\n",
      "Stage:   4 Beta: 0.001 Steps:  14 Acce: 0.256\n",
      "\n",
      "  0%|          | 0/500 [00:00<?, ?it/s]\u001b[A\n",
      " 36%|███▌      | 179/500 [00:00<00:00, 1787.86it/s]\u001b[A\n",
      "100%|██████████| 500/500 [00:00<00:00, 1784.59it/s]\u001b[A\n",
      "Stage:   5 Beta: 0.001 Steps:  15 Acce: 0.259\n",
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      "\n",
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      "Stage:   7 Beta: 0.003 Steps:  18 Acce: 0.242\n",
      "\n",
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      "Stage:   8 Beta: 0.006 Steps:  16 Acce: 0.228\n",
      "\n",
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      "Stage:   9 Beta: 0.009 Steps:  17 Acce: 0.235\n",
      "\n",
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      "Stage:  10 Beta: 0.015 Steps:  17 Acce: 0.234\n",
      "\n",
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      "Stage:  11 Beta: 0.024 Steps:  17 Acce: 0.246\n",
      "\n",
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      "Stage:  12 Beta: 0.038 Steps:  16 Acce: 0.235\n",
      "\n",
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      "Stage:  13 Beta: 0.061 Steps:  17 Acce: 0.260\n",
      "\n",
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      "Stage:  14 Beta: 0.095 Steps:  15 Acce: 0.237\n",
      "\n",
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      "Stage:  15 Beta: 0.149 Steps:  17 Acce: 0.251\n",
      "\n",
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      "Stage:  16 Beta: 0.239 Steps:  15 Acce: 0.243\n",
      "\n",
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      "Stage:  17 Beta: 0.381 Steps:  16 Acce: 0.258\n",
      "\n",
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      "Stage:  18 Beta: 0.600 Steps:  15 Acce: 0.246\n",
      "\n",
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      "Stage:  19 Beta: 0.947 Steps:  16 Acce: 0.291\n",
      "\n",
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      "Stage:  20 Beta: 1.000 Steps:  13 Acce: 0.230\n",
      "\n",
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      "100%|██████████| 500/500 [00:00<00:00, 1505.63it/s]\u001b[A\n",
      "Sample initial stage: ...\n",
      "Stage:   0 Beta: 0.000 Steps:  25 Acce: 1.000\n",
      "\n",
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      "Stage:   1 Beta: 0.000 Steps:  25 Acce: 0.222\n",
      "\n",
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      "Stage:   2 Beta: 0.000 Steps:  18 Acce: 0.250\n",
      "\n",
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      "Stage:   3 Beta: 0.000 Steps:  16 Acce: 0.237\n",
      "\n",
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      "Stage:   4 Beta: 0.000 Steps:  17 Acce: 0.224\n",
      "\n",
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      "Stage:   5 Beta: 0.001 Steps:  18 Acce: 0.225\n",
      "\n",
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      "Stage:   6 Beta: 0.002 Steps:  18 Acce: 0.208\n",
      "\n",
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      "Stage:   7 Beta: 0.003 Steps:  19 Acce: 0.201\n",
      "\n",
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      "Stage:   8 Beta: 0.005 Steps:  20 Acce: 0.222\n",
      "\n",
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      "Stage:   9 Beta: 0.008 Steps:  18 Acce: 0.233\n",
      "\n",
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      "Stage:  10 Beta: 0.013 Steps:  17 Acce: 0.241\n",
      "\n",
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      "Stage:  11 Beta: 0.021 Steps:  16 Acce: 0.243\n",
      "\n",
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      "Stage:  12 Beta: 0.033 Steps:  16 Acce: 0.262\n",
      "\n",
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      "Stage:  13 Beta: 0.052 Steps:  15 Acce: 0.257\n",
      "\n",
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      "Stage:  14 Beta: 0.079 Steps:  15 Acce: 0.243\n",
      "\n",
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      "Stage:  15 Beta: 0.120 Steps:  16 Acce: 0.275\n",
      "\n",
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      "Stage:  16 Beta: 0.181 Steps:  14 Acce: 0.264\n",
      "\n",
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      "Stage:  17 Beta: 0.264 Steps:  15 Acce: 0.276\n",
      "\n",
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      "Stage:  18 Beta: 0.391 Steps:  14 Acce: 0.266\n",
      "\n",
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      "Stage:  19 Beta: 0.597 Steps:  14 Acce: 0.259\n",
      "\n",
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      "Stage:  20 Beta: 0.861 Steps:  15 Acce: 0.260\n",
      "\n",
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      "Stage:  21 Beta: 1.000 Steps:  15 Acce: 0.269\n",
      "\n",
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      "100%|██████████| 500/500 [00:00<00:00, 1843.60it/s]\u001b[A\n",
      "Sample initial stage: ...\n",
      "Stage:   0 Beta: 0.000 Steps:  25 Acce: 1.000\n",
      "\n",
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      "Stage:   1 Beta: 0.000 Steps:  25 Acce: 0.179\n",
      "\n",
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      "Stage:   2 Beta: 0.000 Steps:  23 Acce: 0.183\n",
      "\n",
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      "Stage:   3 Beta: 0.000 Steps:  22 Acce: 0.229\n",
      "\n",
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      "Stage:   4 Beta: 0.000 Steps:  17 Acce: 0.205\n",
      "\n",
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      "Stage:   5 Beta: 0.001 Steps:  20 Acce: 0.220\n",
      "\n",
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      "Stage:   6 Beta: 0.002 Steps:  18 Acce: 0.209\n",
      "\n",
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      "Stage:   7 Beta: 0.003 Steps:  19 Acce: 0.213\n",
      "\n",
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      "Stage:   8 Beta: 0.004 Steps:  19 Acce: 0.244\n",
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     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "# Evaluate the evidence for the various degrees\n",
    "log_Zs = []\n",
    "D = [1, 2, 3, 4, 5]\n",
    "for d in D:\n",
    "    phi = PolynomialBasis(d)\n",
    "    _, _, res = fit_poly(phi, X, y, num_particles=500)\n",
    "    log_Z = np.log(res.model.marginal_likelihood)\n",
    "    log_Zs.append(log_Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "degree 1 gives 25.0212\n",
      "degree 2 gives 41.0753\n",
      "degree 3 gives 142.4574\n",
      "degree 4 gives 139.3597\n",
      "degree 5 gives 137.5729\n"
     ]
    }
   ],
   "source": [
    "for d, log_Z in zip(D, log_Zs):\n",
    "    print('degree %d gives %.4f'%(d, log_Z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 5))\n",
    "_=plt.bar(D, log_Zs, width=0.3)\n",
    "_=plt.xticks(D)\n",
    "plt.xticks(fontsize=20)\n",
    "plt.yticks(fontsize=20)\n",
    "plt.xlabel('Polynomial degree', fontsize=20)\n",
    "plt.ylabel('Model Evidence', fontsize=20)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questions\n",
    "+ The model with degree 3 polynomials has the gradest evidence. However, the degree 4 and 5 seem also very plausible. Is this a problem for the theory of Bayesian model selection? What complicates things here, is that model 3 is included in model 4 which is included in model 5. This requires us to design special priors for the models being right. They have to be consistent in some sense. For example, if model 3 is right then model 4 must be right, etc.\n",
    "\n",
    "+ Revisit the motorcycle dataset problem. Evaluate the model evidence for a 1) Polynomial basis; 2) a Fourier basis; and 3) a Radial basis function basis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Revisiting Challenger Disaster Problem (Model Selection)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Temp (F), O-Ring failure?\n",
      "[[66.  0.]\n",
      " [70.  1.]\n",
      " [69.  0.]\n",
      " [68.  0.]\n",
      " [67.  0.]\n",
      " [72.  0.]\n",
      " [73.  0.]\n",
      " [70.  0.]\n",
      " [57.  1.]\n",
      " [63.  1.]\n",
      " [70.  1.]\n",
      " [78.  0.]\n",
      " [67.  0.]\n",
      " [53.  1.]\n",
      " [67.  0.]\n",
      " [75.  0.]\n",
      " [70.  0.]\n",
      " [81.  0.]\n",
      " [76.  0.]\n",
      " [79.  0.]\n",
      " [75.  1.]\n",
      " [76.  0.]\n",
      " [58.  1.]]\n"
     ]
    }
   ],
   "source": [
    "challenger_data = np.genfromtxt(\"challenger_data.csv\", skip_header=1,\n",
    "                                usecols=[1, 2], missing_values=\"NA\",\n",
    "                                delimiter=\",\")\n",
    "# drop the NA values\n",
    "challenger_data = challenger_data[~np.isnan(challenger_data[:, 1])]\n",
    "\n",
    "# plot it, as a function of temperature (the first column)\n",
    "print(\"Temp (F), O-Ring failure?\")\n",
    "print(challenger_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot it, as a function of temperature (the first column)\n",
    "plt.figure(figsize=(12, 5))\n",
    "plt.plot(challenger_data[:, 0], challenger_data[:, 1], 'ro', \n",
    "         markersize=15)\n",
    "plt.ylabel(\"Damage Incident?\",fontsize=20)\n",
    "plt.xlabel(\"Outside temperature (Fahrenheit)\",fontsize=20)\n",
    "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\",\n",
    "          fontsize=20)\n",
    "plt.yticks([0, 1], fontsize=15)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Challenger space shuttle disaster model:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\n",
       "            \\begin{array}{rcl}\n",
       "            \\text{alpha} &\\sim & \\text{Normal}(\\mathit{mu}=0.0,~\\mathit{sigma}=10.0)\\\\\\text{beta} &\\sim & \\text{Normal}(\\mathit{mu}=0.0,~\\mathit{sigma}=10.0)\\\\\\text{p} &\\sim & \\text{Deterministic}(\\text{Constant},~\\text{Constant},~\\text{alpha},~\\text{beta},~\\text{Constant})\\\\\\text{x} &\\sim & \\text{Bernoulli}(\\mathit{p}=\\text{p})\n",
       "            \\end{array}\n",
       "            $$"
      ],
      "text/plain": [
       "<pymc3.model.Model at 0x14937cba8>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# gather the data and apply preprocessing if any \n",
    "temp = challenger_data[:, 0]\n",
    "temp_scaled = (temp - np.mean(temp))/np.std(temp)\n",
    "data = challenger_data[:, 1]\n",
    "\n",
    "# instantiate the pymc3 model\n",
    "challenger_model = pm.Model()\n",
    "\n",
    "# define the graph \n",
    "with challenger_model:\n",
    "    # define the prior\n",
    "    alpha = pm.Normal('alpha', mu=0., sigma=10.)\n",
    "    beta = pm.Normal('beta', mu=0., sigma=10.)\n",
    "    \n",
    "    # get the probabilities of failure at each observed temp \n",
    "    p = pm.Deterministic('p', 1./(1. + tt.exp(alpha + beta*temp_scaled)))\n",
    "    \n",
    "    # define the likelihood \n",
    "    x = pm.Bernoulli('x', p=p, observed=data)\n",
    "print(\"Challenger space shuttle disaster model:\")\n",
    "challenger_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sample initial stage: ...\n",
      "Stage:   0 Beta: 0.000 Steps:  25 Acce: 1.000\n",
      "\n",
      "  0%|          | 0/500 [00:00<?, ?it/s]\u001b[A\n",
      " 24%|██▍       | 121/500 [00:00<00:00, 1204.65it/s]\u001b[A\n",
      " 48%|████▊     | 239/500 [00:00<00:00, 1195.81it/s]\u001b[A\n",
      " 72%|███████▏  | 360/500 [00:00<00:00, 1199.98it/s]\u001b[A\n",
      "100%|██████████| 500/500 [00:00<00:00, 1192.56it/s]\u001b[A\n",
      "Stage:   1 Beta: 0.011 Steps:  25 Acce: 0.549\n",
      "\n",
      "100%|██████████| 500/500 [00:00<00:00, 5654.91it/s]\n",
      "Stage:   2 Beta: 0.028 Steps:   5 Acce: 0.406\n",
      "\n",
      "  0%|          | 0/500 [00:00<?, ?it/s]\u001b[A\n",
      "100%|██████████| 500/500 [00:00<00:00, 3532.90it/s]\u001b[A\n",
      "Stage:   3 Beta: 0.056 Steps:   8 Acce: 0.346\n",
      "\n",
      "  0%|          | 0/500 [00:00<?, ?it/s]\u001b[A\n",
      "100%|██████████| 500/500 [00:00<00:00, 2808.64it/s]\u001b[A\n",
      "Stage:   4 Beta: 0.106 Steps:  10 Acce: 0.301\n",
      "\n",
      "  0%|          | 0/500 [00:00<?, ?it/s]\u001b[A\n",
      " 48%|████▊     | 240/500 [00:00<00:00, 2394.73it/s]\u001b[A\n",
      "100%|██████████| 500/500 [00:00<00:00, 2361.99it/s]\u001b[A\n",
      "Stage:   5 Beta: 0.182 Steps:  12 Acce: 0.275\n",
      "\n",
      "  0%|          | 0/500 [00:00<?, ?it/s]\u001b[A\n",
      " 41%|████      | 205/500 [00:00<00:00, 2048.77it/s]\u001b[A\n",
      "100%|██████████| 500/500 [00:00<00:00, 2041.58it/s]\u001b[A\n",
      "Stage:   6 Beta: 0.313 Steps:  14 Acce: 0.266\n",
      "\n",
      "  0%|          | 0/500 [00:00<?, ?it/s]\u001b[A\n",
      " 42%|████▏     | 212/500 [00:00<00:00, 2117.50it/s]\u001b[A\n",
      "100%|██████████| 500/500 [00:00<00:00, 2076.29it/s]\u001b[A\n",
      "Stage:   7 Beta: 0.529 Steps:  14 Acce: 0.250\n",
      "\n",
      "  0%|          | 0/500 [00:00<?, ?it/s]\u001b[A\n",
      " 39%|███▉      | 196/500 [00:00<00:00, 1959.82it/s]\u001b[A\n",
      "100%|██████████| 500/500 [00:00<00:00, 1943.86it/s]\u001b[A\n",
      "Stage:   8 Beta: 0.897 Steps:  15 Acce: 0.270\n",
      "\n",
      "  0%|          | 0/500 [00:00<?, ?it/s]\u001b[A\n",
      " 42%|████▏     | 209/500 [00:00<00:00, 2085.22it/s]\u001b[A\n",
      "100%|██████████| 500/500 [00:00<00:00, 2060.88it/s]\u001b[A\n",
      "Stage:   9 Beta: 1.000 Steps:  14 Acce: 0.261\n",
      "\n",
      "  0%|          | 0/500 [00:00<?, ?it/s]\u001b[A\n",
      " 38%|███▊      | 192/500 [00:00<00:00, 1912.39it/s]\u001b[A\n",
      "100%|██████████| 500/500 [00:00<00:00, 1860.62it/s]\u001b[A\n"
     ]
    }
   ],
   "source": [
    "num_particles = 500\n",
    "trace, smc = sample_smc(model=challenger_model, \n",
    "                           draws=num_particles,\n",
    "                          threshold=0.8, \n",
    "                          progressbar=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "  0%|          | 0/500 [00:00<?, ?it/s]\u001b[A\n",
      "100%|██████████| 500/500 [00:00<00:00, 3612.98it/s]\u001b[A\n"
     ]
    }
   ],
   "source": [
    "ppsamples = pm.sample_posterior_predictive(model=challenger_model, \n",
    "                                           trace=trace, \n",
    "                                           var_names=['p'])['p']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ppmean = ppsamples.mean(0)\n",
    "pp_lower, pp_upper = np.percentile(ppsamples, axis=0, q=[2.5, 97.5])\n",
    "\n",
    "plt.figure(figsize=(15, 8))\n",
    "plt.plot(temp, data, 'ro', markersize=12, label='Observed data')\n",
    "idx=np.argsort(temp)\n",
    "plt.plot(temp[idx], ppmean[idx], linestyle='--', linewidth=2.5, \n",
    "         label='Post. pred. mean prob.')\n",
    "plt.fill_between(temp[idx], pp_lower[idx], pp_upper[idx], \n",
    "                color='purple', alpha=0.25, label='95% Confidence')\n",
    "plt.ylabel(\"Probability estimate\",fontsize=20)\n",
    "plt.xlabel(\"Outside temperature (Fahrenheit)\",fontsize=20)\n",
    "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\",\n",
    "          fontsize=20)\n",
    "plt.yticks(np.arange(0., 1.01, 0.2), fontsize=20)\n",
    "plt.xticks(fontsize=20)\n",
    "plt.legend(loc='best', fontsize=20)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "logZ_temp = np.log(smc.model.marginal_likelihood)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
